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The operator amenability of $$A(G)$$. (English) Zbl 0842.43004
Let $$G$$ be a locally compact group and $$A(G)$$ its Fourier algebra. The main results in this paper are: (1) $$A(G)$$ is operator amenable for every compact group $$G$$; (2) the group $$G$$ is amenable if and only if $$A(G)$$ is operator amenable; (3) the $$C^*$$-algebra $$A$$ is Banach algebra amenable if and only if $$A$$ is operator amenable.

##### MSC:
 43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. 22D15 Group algebras of locally compact groups
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